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If `alpha` is the only real root of the equation `x^(3) + bx^(2) + cx + 1 = 0 (b lt c)`, then find the value of `tan^(-1) alpha + tan^(-1) (alpha^(-1))`

A

`-pi`

B

`- pi/2`

C

`pi/2`

D

`pi`

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The correct Answer is:
A
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